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Entry  Mon Aug 22 20:18:21 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise CTN_Thermo-Optic_Noise_Study.pdf
    Reply  Tue Aug 23 19:56:21 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise CTN_Thermo-Optic_Noise_Study.pdf
       Reply  Tue Aug 23 22:04:24 2022, awade, Summary, NoiseBudget, Birefringence noise in thermo-optic noise 
          Reply  Thu Aug 25 19:38:01 2022, Anchal, Summary, NoiseBudget, Birefringence noise in thermo-optic noise 
       Reply  Thu Aug 25 19:19:27 2022, Anchal, Summary, NoiseBudget, Looking at the measured and estimated photothermal transfer functions CTN_Photothermal_TF_with_TPE.pdfCTN_Thermo-Optic_Noise_Study.pdf
          Reply  Fri Aug 26 15:56:38 2022, Anchal, Summary, NoiseBudget, Checking with Martin Fejer's calculations CTN_Photothermal_TF_with_TPE.pdfCTN_Thermo-Optic_Noise_Study.pdf
Message ID: 2612     Entry time: Mon Aug 22 20:18:21 2022     Reply to this: 2613
Author: Anchal 
Type: Summary 
Category: NoiseBudget 
Subject: Birefringence noise in thermo-optic noise 

I followed the analysis of this recently published paper Jan Meyer et al 2022 Class. Quantum Grav. 39 135001 to calculate the birefringence noise in the CTN experiment. Interestingly, the contribution from birefringence noise after my first attempt at this calculation looks very close to what we were calculating as coating thermo-refractive noise before. If this were true, our experiment would have seen it much before. In fact, we wouldn't have seen thermo-optic cancellation as Tara experimentally verified here. So something is missing

What is birefringence noise?

After going through some literature and reading properly Meyer et al, I have the following understanding of the birefringence noise (and why it is called so).

  • The temperature fluctuations cause length fluctuations in the coating layers (through the coefficient of thermal expansion)
  • The length fluctuations cause stress fluctuations in the coating layers (through Young's modulus Y).
  • The stress fluctuations get converted into refractive index fluctuations through the photoelastic effect (through photoelastic tensor)
  • The photoelastic tensor for cubic crystals like GaAs has 3 independent values, P11, P12 and P44. (Section 12: Table 1. Elasto-Optic Coefficients: Cubic Crystals (43m, 432, m3m))
  • This induces refractive index fluctuations that are different for the fast and slow axes. The difference between the two fluctuations causes a phase shift in reflected light from each layer. That's why this can be birefringence noise. In an unstressed isotropic material, this pathway should not exist.

Is this different from thermo-refractive noise?

This is a question I am still not sure how to answer. My understanding is that the common mode change in refractive indices of both axes drives the thermo-refractive noise. This means I should be able to derive the coefficient of thermo-refraction using the same formalism.


Both thermo-refractive noise and thermo-photoelastic noise show up as dn/dT terms in the thermo-optic noise summation, just through different physical processes. This could mean that experimentally measured coefficients of thermo-refraction already include birefringent contribution if any. In my calculations for the plots presented here, I got the following values of the two coefficients:

Coefficient of thermo-refraction (Effective for coating): 8.289e-05

Coefficient of thermo-photoelastic effect (Effective for coating, using Eq.11 of Meyer et al.): 8.290e-05

It was very surprising to me to see that both these coefficients came out to be within 1% of each other.

Because of this, when we add the noise sources coherently (since they are all driven by the same thermal fluctuations), the thermo-optic cancellation that we have experimentally proved does not work anymore. So something must be wrong with my calculation.

Possible explanations:

  • Calculaiton error in my code. I'll double check tomorrow.
  • Somehow the thermorefractive noise already takes into account the birefringent noise, through the coefficient of thermo-refraciton that we use as seed in our thermo-refractive noise calculation. This would explain how the witnessed themo-optic cancellation was achieved.
  • Meyer et al. is calculating birefringent noise for the substrate. Maybe the tensorial calculations are different for coatings.




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